In order to obtain conditional maximum likelihood estimates, the so-called conditioning estimates have to be calculated. In this paper a method is examined that does not calculate these constants exactly, but approximates them using Monte Carlo Markov Chains. As an example, the method is applied to the conditional estimation of both item and person parameters in the Rasch model. The key idea for this approach was developed by C. J. Geyer and E. A. Thompson (1992), who showed that, in the exponential family, a quantity that is proportional to the conditioning constant can be expressed as an expectation with respect to a certain distribution. Simulating from this distribution, an estimate of the proportional quantity can be obtained as the observed sample mean. Inserting this estimate into the conditional likelihood then allows one to maximize the approximate likelihood, as the proportionality constant does not depend on the parameters to be estimated. (Contains 5 tables, 1 figure, and 11 references.) (Author/SLD)